2021/06/14 by Amine Bohi, Guillaume Auzias, Bohi, Amine +3
Computer Science · Mathematics · #Biological Physics (physics.bio-ph) #Computer Graphics and Visualization Techniques #Computer Vision and Pattern Recognition (cs.CV) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Medical Image Segmentation Techniques #Medical Physics (physics.med-ph) #Morphological variations and asymmetry
paper · doi:10.48550/arxiv.2106.07470
openalex publication_date 2021/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the vector fields from the original surfaces onto a common domain. In this paper, we propose a framework to achieve this task by mapping the vector fields onto a common space, using some notions of differential geometry. The proposed framework enables the computation of statistics on vector fields. We demonstrate its interest in practice with an application on real data with a quantitative assessment of the reproducibility of curvature directions that describe the complex geometry of cortical folding patterns. The proposed framework is general and can be applied to different types of vector fields and surfaces, allowing for a large number of high potential applications in medical imaging.